On the Riemann tensor in double field theory
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Author(s)
Hohm, Olaf
Zwiebach, Barton
Date Issued
May 2012
Journal
Journal of High Energy Physics
Publisher
Springer-Verlag
Citation
Hohm, Olaf, and Barton Zwiebach. “On the Riemann Tensor in Double Field Theory.” Journal of High Energy Physics 2012.5 (2012).
Version
Author's final manuscript
Abstract
Double field theory provides T-duality covariant generalized tensors that are natural extensions of the scalar and Ricci curvatures of Riemannian geometry. We search for a similar extension of the Riemann curvature tensor by developing a geometry based on the generalized metric and the dilaton. We find a duality covariant Riemann tensor whose contractions give the Ricci and scalar curvatures, but that is not fully determined in terms of the physical fields. This suggests that α′ corrections to the effective action require α′ corrections to T-duality transformations and/or generalized diffeomorphisms. Further evidence to this effect is found by an additional computation that shows that there is no T-duality invariant four-derivative object built from the generalized metric and the dilaton that reduces to the square of the Riemann tensor.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/jhep05(2012)126
